2n^2+128=32n

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Solution for 2n^2+128=32n equation:


Simplifying
2n2 + 128 = 32n

Reorder the terms:
128 + 2n2 = 32n

Solving
128 + 2n2 = 32n

Solving for variable 'n'.

Reorder the terms:
128 + -32n + 2n2 = 32n + -32n

Combine like terms: 32n + -32n = 0
128 + -32n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(64 + -16n + n2) = 0

Factor a trinomial.
2((8 + -1n)(8 + -1n)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8

Subproblem 2

Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8

Solution

n = {8, 8}

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